Hi! I’m looking for some feedback on what skills I should use in my standards-based grading Algebra 2 with Trigonometry (A2T) course spring semester. I just threw together the following list as a rough draft, and do expect to edit it extensively over the coming week.

A note on organization: I’m planning to focus on algebra third quarter and analysis fourth quarter (did I miscategorize any skills?). Fourth quarter tends to be the shortest quarter, mainly due to our state standardized tests, so it has fewer skills. The first six skills each quarter are meant to be prerequisite skills from Algebra I, Geometry, or even middle-school math; I will hold students accountable for knowing and remembering these skills, but aside from a miniature review I do not intend to teach skills #1-6. I’ve italicized skills that seem weak or a little too easy, and may be combined with others or even eliminated. I’ve bolded skills that seem more advanced or non-essential and possibly not for every student. I’m toying with the idea of requiring students demonstrate mastery of certain numbers of core skills and advanced skills to earn different letter grades.

**ALGEBRA (especially of the second degree)!**

** **

- Graph a line given its equation
- Determine the equation of a line from its graph
- Solve a linear equation in any form
- Solve a system of two linear equations
- Manipulate algebraic expressions to simplify or expand
- Substitute numbers for variables in an algebraic expression
*Convert between scientific and standard notations of numbers**Find the degree and leading coefficient of a polynomial*- Combine like terms to add or subtract polynomials
- Use the distributive property to multiply polynomials
**Use long division to divide polynomials**- Factor a monic quadratic expression
**Factor a quadratic expression with any leading coefficient***Characterize the shape of a parabola given its equation*- Determine the equation of a parabola given its graph
*Solve quadratic equations in factored form using the zero product property*- Solve quadratic equations in standard form using the quadratic formula
**Solve quadratic equations in standard form by completing the square***Combine like terms to get an equation in standard form***Plot a complex number in the complex plane****Add and subtract complex numbers****Multiply complex numbers****Determine the magnitude of a complex number****Solve quadratic equations with complex roots**- Add and subtract matrices, and multiply a matrix by a scalar
- Multiply matrices
- Find matrix determinants
**Find the inverse of a matrix****Solve matrix equations**- Solve systems of linear equations
- Graph linear inequalities
**Solve systems of linear inequalities by linear programming****Plot the graph of various conic sections based on its equation****Identify key characteristics of each conic section****Explain the relationship among the conic sections**

**ANALYSIS (including TRIGONOMETRY)!**

** **

- Determine a function’s domain, range, maxima, and minima
- Determine a function’s zeros and y-intercepts
- Determine the end behavior of a function
- Convert between tables of values, equations, and graphs of functions
- Apply the Pythagorean Theorem to find unknown sides in right triangles
- Use trigonometry to find unknown sides & angles in right triangles
- Use laws of sines and cosines to find unknown sides & angles in any triangle
**Solve entire triangles given three pieces of information**- Apply triangular trigonometry to real-world scenarios
*Draw and measure angles in standard position*- Convert between degrees and radians
- Find coordinates and slope where an angle meets the unit circle
- Solve trigonometric equations (including multiple solutions)
**Use common trigonometric identities**- Sketch the graph of trigonometric functions
- Find period and amplitude of periodic functions
**Plot points using polar coordinates****Convert between polar and Cartesian coordinates****Plot various polar functions**- Evaluate exponential expressions
- Apply the rules of exponents to simplify an expression
- Identify characteristics of exponential functions
- Use exponential functions to model real-world scenarios
*Convert between exponential and logarithmic equations*- Evaluate logarithmic expressions
- Apply the rules of logarithms to simplify an expression
- Solve exponential and logarithmic equations
**Use logistic growth to model real-world scenarios**- Identify the effects of common function transformations
**Graph functions and their inverses**- Use inverse operations to solve equations
**Compose functions****Discuss the effect of transforming, inverting, and composing functions on domain and range**

I’m looking for feedback of any kind now, all the way from how to rephrase a skill better and more specifically, to what quintessential A2T skills are missing that I need to add right away. Also, are there some skills here that I can get rid of entirely? Even with the idea of prerequisite/core/advanced skills, 73 seems like way too many (I had only 32 skills this fall for geometry).

[PS I promise a post up soon reflecting back on what worked and what didn’t from semester 1’s courses, and looking ahead to my plans for the new semester’s courses, including how those plans reflect on SBG and PBL.]

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